Displaying similar documents to “On an estimate of a functional in the class of holomorphic univalent functions”

On the estimate of the fourth-order homogeneous coefficient functional for univalent functions

Larisa Gromova, Alexander Vasil'ev (1996)

Annales Polonici Mathematici

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The functional |c₄ + pc₂c₃ + qc³₂| is considered in the class of all univalent holomorphic functions f ( z ) = z + ∑ n = 2 ∞ c n z n in the unit disk. For real values p and q in some regions of the (p,q)-plane the estimates of this functional are obtained by the area method for univalent functions. Some new regions are found where the Koebe function is extremal.

Coefficient inequalities for concave and meromorphically starlike univalent functions

B. Bhowmik, S. Ponnusamy (2008)

Annales Polonici Mathematici

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Let denote the open unit disk and f: → ℂ̅ be meromorphic and univalent in with a simple pole at p ∈ (0,1) and satisfying the standard normalization f(0) = f’(0)-1 = 0. Also, assume that f has the expansion f ( z ) = ∑ n = - 1 ∞ a ₙ ( z - p ) ⁿ , |z-p| < 1-p, and maps onto a domain whose complement with respect to ℂ̅ is a convex set (starlike set with respect to a point w₀ ∈ ℂ, w₀ ≠ 0 resp.). We call such functions concave (meromorphically starlike resp.) univalent functions and denote this class by C o ( p ) ( Σ s ( p , w ₀ ) resp.). We prove...

A note on Briot-Bouquet-Bernoulli differential subordination

Stanisława Kanas, Joanna Kowalczyk (2005)

Commentationes Mathematicae Universitatis Carolinae

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Let p , q be analytic functions in the unit disk 𝒰 . For α ∈ [ 0 , 1 ) the authors consider the differential subordination and the differential equation of the Briot-Bouquet type: p 1 - α ( z ) + z p ' ( z ) δ p α ( z ) + λ p ( z ) ≺ h ( z ) , z ∈ 𝒰 , q 1 - α ( z ) + n z q ' ( z ) δ q α ( z ) + λ q ( z ) = h ( z ) , z ∈ 𝒰 , with p ( 0 ) = q ( 0 ) = h ( 0 ) = 1 . The aim of the paper is to find the dominant and the best dominant of the above subordination. In addition, the authors give some particular cases of the main result obtained for appropriate choices of functions h .